Saddle Point
Back to the cover

Part I · Foundations

  1. 0 Mathematical Foundations
  2. 1 Observation, Beliefs, and Decision

Part II · Engines

  1. 2 Competing for Allocation: The Blotto Game
  2. 3 Bargaining, Commitment, and Repeated Cooperation
  3. 4 Signals, Disclosure, and Persuasion
  4. 5 Different Models of One Game
  5. 6 Leadership and Rules: Inspection
  6. 7 Decisions in Time
  7. 8 Many Agents
  8. 9 Networks, Dependence, and Resilience
  9. 10 Aggregating Information

Part III · Systems

  1. 11 Architecture of Decision Support
  2. 12 Simulation and Wargaming with AI Agents

Part IV · Limits

  1. 13 Where the Mathematics Stops
Frederick W. Lanchester

Chapter 7 · Decisions in Time

Frederick W. Lanchester

1868 – 1946

Photograph: Birmingham Museums Trust, Frederick W. Lanchester, date unknown, CC BY-SA 4.0, via Wikimedia Commons. Shown toned. File and licence

The problem on the desk

Writing about aircraft and warfare, Lanchester asked what concentration of forces changes mathematically. His aimed-fire model made fighting strength depend on the square of numbers under its stated assumptions.1

A life in moments

  1. 1868

    Lewisham

    Born on 23 October.2

  2. 1885

    Normal School of Science · South Kensington

    Won a scholarship; later left without completing the final examinations.3

  3. 1889

    Forward Gas Engine Company · Birmingham

    Began engineering work on engines.4

  4. 1895

    Birmingham

    Tested his first motor car on the road.5

  5. 1907–1908

    Published the two volumes of Aerial Flight.6

  6. 1914

    Dated his chapter on concentration of forces 2 October.7

  7. 1916

    Published Aircraft in Warfare.8

  8. 1946

    Died on 8 March.9

Every line rests on a dated source (numbered below) unless it carries a mark: R for an inference, S for a story as told.

In their own words

One of the great questions at the root of all strategy is that of concentration

Aircraft in Warfare: The Dawn of the Fourth Arm, 191611

A story

Testing from the window

In 1894 Lanchester tested model gliders from an upper window, moving between engineering experiments and his developing theory of flight.10

The card in the book

English engineer. He built one of the first British petrol motor cars and founded the Lanchester Engine Company, and his two-volume Aerial Flight developed the circulation theory of lift. In Aircraft in Warfare (1916) he proposed the differential equations of attrition now named after him and derived the -square law, the quantitative case for concentration. M. Osipov published a closely related analysis independently in a Russian military journal in 1915.

Main works Aerial Flight (1907–08); Aircraft in Warfare: The Dawn of the Fourth Arm (1916).

To read further

Sources (11)
  1. Aircraft in Warfare: The Dawn of the Fourth Arm, Frederick W. Lanchester, 1916; Chapter V, pp. 39–49, §§19–23; chapter dated 2 October 1914
  2. Frederick Lanchester: Timeline, Coventry University, Lanchester Interactive Archive; 1868 entry
  3. Frederick Lanchester: Timeline, Coventry University, Lanchester Interactive Archive; 1885 entry
  4. Frederick Lanchester: Timeline, Coventry University, Lanchester Interactive Archive; 1889 entry
  5. Frederick Lanchester: Timeline, Coventry University, Lanchester Interactive Archive; 1895 entry
  6. Frederick Lanchester: Timeline, Coventry University, Lanchester Interactive Archive; 1907–1908 entries
  7. Aircraft in Warfare: The Dawn of the Fourth Arm, Frederick W. Lanchester, 1916; Chapter V heading
  8. Aircraft in Warfare: The Dawn of the Fourth Arm, Frederick W. Lanchester, 1916; Title page
  9. Frederick Lanchester: Timeline, Coventry University, Lanchester Interactive Archive; 1946 entry
  10. Frederick Lanchester: Timeline, Coventry University, Lanchester Interactive Archive; 1894 entry
  11. Aircraft in Warfare: The Dawn of the Fourth Arm, Frederick W. Lanchester, 1916; p. 39, §19; excerpt

The facts on this page were gathered for the site from the sources listed, each checked against its locator; the book's card is reproduced unchanged.